Lazy Nonlinear Diffusion Parameter Estimation

  • Daniel Thuerck
  • Arjan Kuijper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8156)


Perona–Malik diffusion is a well-known type of nonlinear diffusion that can be used for image segmentation and denoising. The process itself needs an parameter k to decide which edges will be retained and which can be blurred and a stopping time t S . Although there have been investigations on how to set these parameters, especially for regularized diffusion models, as well as different criteria for the optimal stopping time have been suggested, there is yet no quick and conclusive way to estimate both parameters – or to reduce the search space at least. In this paper, we show that Gaussian noise characteristics of an image and the diffusion parameters for an optimal optical result can be estimated based on the image histogram. We demonstrate the effectiveness of lazy learning in this area and develop a custom feature weighting algorithm.


Nonlinear Diffusion Average Absolute Error Lazy Learning Estimate Noise Variance Nonlinear Anisotropic Diffusion 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


  1. 1.
    Gilboa, G., Sochen, N.A., Zeevi, Y.Y.: Estimation of optimal pde-based denoising in the SNR sense. IEEE Transactions on Image Processing 15(8), 2269–2280 (2006)CrossRefGoogle Scholar
  2. 2.
    Guo, Z., Sun, J., Zhang, D., Wu, B.: Adaptive Perona-Malik model based on the variable exponent for image denoising. IEEE TIP 21(3), 958–967 (2012), MathSciNetGoogle Scholar
  3. 3.
    Halland, M., Frank, E., Holmes, G., Pfahringer, B., Reutemann, P., Witten, I.H.: The WEKA data mining software: An update. In: ACM SIGKDD Explorations, vol. 11, pp. 10–18 (2009)Google Scholar
  4. 4.
    Kichenassamy, S.: The Perona-Malik method as an edge pruning algorithm. Journal of Mathematical Imaging and Vision 30, 209–219 (2008)MathSciNetCrossRefGoogle Scholar
  5. 5.
    Kuijper, A.: p-Laplacian driven image processing. In: 14th International Conference on Image Processing, ICIP 2007, vol. V, pp. 257–260 (2007)Google Scholar
  6. 6.
    Kuijper, A.: Geometrical PDEs based on second order derivatives of gauge coordinates in image processing. Image and Vision Computing 27(8), 1023–1034 (2009)CrossRefGoogle Scholar
  7. 7.
    Monteil, J., Beghdadi, A.: A new interpretation and improvement of the nonlinear anisotropic diffusion for image enhancement. IEEE TPAMI 21(9), 940–946 (1999)CrossRefGoogle Scholar
  8. 8.
    Mrázek, P., Navara, M.: Selection of optimal stopping time for nonlinear diffusion filtering. International Journal of Computer Vision 52(2-3), 189–203 (2003)CrossRefGoogle Scholar
  9. 9.
    Ndajah, P., Kikuchi, H., Yukawa, M., Watanabe, H., Muramatsu, S.: An investigation on the quality of denoised images. Circuits, Systems and Signal Processing 5, 423–434 (2011)Google Scholar
  10. 10.
    Perona, P., Malik, J.: Scale-space and edge detection using anisotropic diffusion. IEEE Transactions on Pattern Analysis and Machine Intelligence 12, 629–639 (1990)CrossRefGoogle Scholar
  11. 11.
    Quinlan, J.R.: Learning with continuous classes. In: Proceedings of the Australian Joint Conference on Artificial Intelligence, pp. 343–348 (1992)Google Scholar
  12. 12.
    Rudin, L.I., Osher, S., Fatemi, E.: Nonlinear total variation based noise removal algorithms. Physica D 60(259-268) (1992)Google Scholar
  13. 13.
    Schwarzkopf, A., Kalbe, T., Bajaj, C., Kuijper, A., Goesele, M.: Volumetric nonlinear anisotropic diffusion on gpus. In: Bruckstein, A.M., ter Haar Romeny, B.M., Bronstein, A.M., Bronstein, M.M. (eds.) SSVM 2011. LNCS, vol. 6667, pp. 62–73. Springer, Heidelberg (2012)CrossRefGoogle Scholar
  14. 14.
    Shao, H., Zou, H.: Threshold estimation based on Perona-Malik model. In: Int. Conf. on Computational Intelligence and Software Engineering, pp. 1–4 (2009)Google Scholar
  15. 15.
    Thuerck, D., Kuijper, A.: Cosine-driven non-linear denoising. In: Kamel, M., Campilho, A. (eds.) ICIAR 2013. LNCS, vol. 7950, pp. 245–254. Springer, Heidelberg (2013)CrossRefGoogle Scholar
  16. 16.
    Voci, F., Eiho, S., Sugimoto, N., Sekibuchi, H.: Estimating the gradient in the Perona-Malik equation. IEEE Signal Processing Magazine 21(3), 39–65 (2004), CrossRefGoogle Scholar
  17. 17.
    Weickert, J.: Coherence-enhancing diffusion of colour images. Image Vision Comput. 17(3-4), 201–212 (1999)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Daniel Thuerck
    • 1
  • Arjan Kuijper
    • 1
    • 2
  1. 1.TU DarmstadtGermany
  2. 2.Fraunhofer IGDDarmstadtGermany

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